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Identifier

St001635: Posets ⟶ ℤ

Values

([],1) => 1

([],2) => 2

([(0,1)],2) => -1

([],3) => 3

([(1,2)],3) => 0

([(0,1),(0,2)],3) => -1

([(0,2),(2,1)],3) => -1

([(0,2),(1,2)],3) => -1

([],4) => 4

([(2,3)],4) => 1

([(1,2),(1,3)],4) => 0

([(0,1),(0,2),(0,3)],4) => 1

([(0,2),(0,3),(3,1)],4) => -1

([(0,1),(0,2),(1,3),(2,3)],4) => 1

([(1,2),(2,3)],4) => 0

([(0,3),(3,1),(3,2)],4) => 1

([(1,3),(2,3)],4) => 0

([(0,3),(1,3),(3,2)],4) => 1

([(0,3),(1,3),(2,3)],4) => 1

([(0,3),(1,2)],4) => -2

([(0,3),(1,2),(1,3)],4) => -1

([(0,2),(0,3),(1,2),(1,3)],4) => 4

([(0,3),(2,1),(3,2)],4) => -1

([(0,3),(1,2),(2,3)],4) => -1

([],5) => 5

([(3,4)],5) => 2

([(2,3),(2,4)],5) => 1

([(1,2),(1,3),(1,4)],5) => 2

([(0,1),(0,2),(0,3),(0,4)],5) => 5

([(0,2),(0,3),(0,4),(4,1)],5) => 1

([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1

([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 5

([(1,3),(1,4),(4,2)],5) => 0

([(0,3),(0,4),(4,1),(4,2)],5) => 1

([(1,2),(1,3),(2,4),(3,4)],5) => 2

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1

([(0,3),(0,4),(3,2),(4,1)],5) => -1

([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1

([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 5

([(2,3),(3,4)],5) => 1

([(1,4),(4,2),(4,3)],5) => 2

([(0,4),(4,1),(4,2),(4,3)],5) => 5

([(2,4),(3,4)],5) => 1

([(1,4),(2,4),(4,3)],5) => 2

([(0,4),(1,4),(4,2),(4,3)],5) => 5

([(1,4),(2,4),(3,4)],5) => 2

([(0,4),(1,4),(2,4),(4,3)],5) => 5

([(0,4),(1,4),(2,4),(3,4)],5) => 5

([(0,4),(1,4),(2,3)],5) => -2

([(0,4),(1,3),(2,3),(2,4)],5) => -1

([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 6

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 17

([(0,4),(1,4),(2,3),(4,2)],5) => 1

([(0,4),(1,3),(2,3),(3,4)],5) => 1

([(0,4),(1,4),(2,3),(2,4)],5) => 1

([(0,4),(1,4),(2,3),(3,4)],5) => 1

([(1,4),(2,3)],5) => -1

([(1,4),(2,3),(2,4)],5) => 0

([(0,4),(1,2),(1,4),(2,3)],5) => -1

([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1

([(1,3),(1,4),(2,3),(2,4)],5) => 5

([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 6

([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 5

([(0,4),(1,2),(1,4),(4,3)],5) => 1

([(0,4),(1,2),(1,3)],5) => -2

([(0,4),(1,2),(1,3),(1,4)],5) => 1

([(0,2),(0,4),(3,1),(4,3)],5) => -1

([(0,4),(1,2),(1,3),(3,4)],5) => -1

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 1

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1

([(0,3),(0,4),(1,2),(1,4)],5) => -1

([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 6

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 17

([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2

([(0,3),(1,2),(1,4),(3,4)],5) => -1

([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 6

([(1,4),(3,2),(4,3)],5) => 0

([(0,3),(3,4),(4,1),(4,2)],5) => 1

([(1,4),(2,3),(3,4)],5) => 0

([(0,4),(1,2),(2,4),(4,3)],5) => 1

([(0,3),(1,4),(4,2)],5) => -2

([(0,4),(3,2),(4,1),(4,3)],5) => 1

([(0,4),(1,2),(2,3),(2,4)],5) => 1

([(0,4),(2,3),(3,1),(4,2)],5) => -1

([(0,3),(1,2),(2,4),(3,4)],5) => -1

([(0,4),(1,2),(2,3),(3,4)],5) => -1

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1

([],6) => 6

([(4,5)],6) => 3

([(3,4),(3,5)],6) => 2

([(2,3),(2,4),(2,5)],6) => 3

([(1,2),(1,3),(1,4),(1,5)],6) => 6

([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 11

([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 5

([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 3

([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 5

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 11

([(1,3),(1,4),(1,5),(5,2)],6) => 2

([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 3

([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2

([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 6

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Description

The trace of the square of the Coxeter matrix of the incidence algebra of a poset.

Code

def statistic(P):
     return (P.coxeter_transformation()^2).trace()

Created

Oct 07, 2020 at 22:11 by Martin Rubey

Updated

Oct 07, 2020 at 22:11 by Martin Rubey